The illusion of inefficiency: ghost artefacts and neglected nonlinearity in G20 equities

Under the Adaptive Market Hypothesis, rolling-window BDS test rejections are often read as evidence of genuine, time-varying inefficiency. This study uses a computationally exhaustive framework to test that claim across 19 individual G20 equity markets and shows that most such rejections are instead statistical artefacts of suboptimal prewhitening and an uncalibrated significance threshold. Evaluating 108 Gaussian and non-Gaussian ARMA-GARCH permutations neutralizes volatility distortions, and calibrating the underlying test’s own averaged p-value corrects it to a formally valid threshold. Together, these two corrections revert fourteen of nineteen markets to weak-form efficiency. Monte Carlo simulations expose a severe trade-off. The expansive filters needed to eliminate false positives also degrade statistical power to detect genuine nonlinear-in-mean dynamics. The residual inefficiency that survives this filtering in the remaining five markets, identified via an i.i.d. bootstrap on standardized residuals, is therefore best read as a conservative lower bound rather than an absolute measure of inefficiency. Of these five, Canada’s classification is particularly difficult to separate from residual filter inadequacy, unlike Australia’s. Finally, first-moment persistence is more temporally unstable than second-moment persistence in 16 of 19 markets, a pattern that may reflect the indices’ own data-generating processes, the methodological pipeline’s design, or both.